The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is -
A. 30
B. 33
C. 36
D. 45
Answer: Option B
Solution(By Examveda Team)
Let the 3 consecutive number isx, x + 1, x + 2
According to question,
$$ \Rightarrow {x^2} + {\left( {x + 1} \right)^2} + {\left( {x + 2} \right)^2}$$ = 365
$$ \Rightarrow {x^2} + {x^2} + 1 + 2x + {x^2} + 4 + 4x$$ = 365
$$\eqalign{ & \Rightarrow 3{x^2} + 6x = 360 \cr & \Rightarrow {x^2} + 2x - 120 = 0 \cr & \Rightarrow \left( {x - 10} \right)\left( {x + 12} \right) = 0 \cr & \Rightarrow x = 10 \cr & {\text{Sum of numbers :}} \cr & = 10 + 11 + 12 \cr & = 33 \cr} $$
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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